How do I change the word Permalink to an image?
Permalink means Nothing to normal people. It only means something to us WordPress users. I need to change the word Permalink to a comment image so people know that they click on that to comment.

Also when Reply is click an error shows up saying that P2 isn't connected to the server, but of course when Permalinks is clicked it works perfectly fine. ("Whoops! Looks like you are not connected to the server. P2 could not connect with WordPress.")

The word "Permalink" is contained in the file entry.php. Create a copy of this file and place it in your child theme folder. Have a look at line 37 and replace Permalink with other text of your choosing in this function: <?php _e( 'Permalink', 'p2' ); ?>

Also when Reply is click an error shows up saying that P2 isn't connected to the server, but of course when Permalinks is clicked it works perfectly fine. ("Whoops! Looks like you are not connected to the server. P2 could not connect with WordPress.")

Does this happen whether you are logged into your account or not?

I've clicked on your comment link several times and haven't seen the error yet.